A PDFA is minimal if any other PDFA that computes the same function has no less states [1]}. The simple PDFA in Fig. REF  is minimal since clearly the function cannot be computed by a PDFA with a single state.
Based on \(\equiv \)  we define a weaker notion of minimality as follows. A PDFA \(A\)  is said to be weakly minimal if for every \(q, q^{\prime } \in Q\) , \(q\lnot \equiv q^{\prime }\) .By definition, for every PDFA \(A\) , \(A{/_{\scriptscriptstyle \equiv }}\)  is weakly minimal.
